RecurrenceTable

A table of the values of a sequence defined by a recurrence equation and initial conditions.

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RecurrenceTable(eqns, a, {n, nmin, nmax})

a(nmin), \dots, a(nmax)

, given

eqns

: one general recurrence equation over

a

plus its initial conditions.

Typed signatures

Type	Package	Applies
`(eqns: list<any>, a: any, spec: list<any>) -> list<any>`	`combinatorics`	always

Domain: Collections

Details

$eqns$ mixes literal-index equations (initial conditions, $a(1) = 7$ ) with exactly one general equation whose index mentions $n$ ( $a(n+1) = 3\,a(n)$ , or plainly $a(n) = a(n-1) + a(n-2)$ ) — only a single recurrence order is supported, not a piecewise definition.
$a$ never needs to be declared as a head: it is read directly out of $eqns$ and resolved by walking the recurrence, not by evaluating $a(n)$ as an ordinary compute-engine call.
See LinearRecurrence for the constant-coefficient case without writing out the equations.

Examples

Basic #

a geometric sequence

\mathrm{RecurrenceTable}(\begin{cases}a(n+1)=3a(n)\\a(1)=7\end{cases}, a, \bigl\lbrack n, 1, 5\bigr\rbrack)

Out

\bigl\lbrack7, 21, 63, 189, 567\bigr\rbrack

Scope #

the Fibonacci recurrence

\mathrm{RecurrenceTable}(\begin{cases}a(n)=a(n-1)+a(n-2)\\a(1)=1\\a(2)=1\end{cases}, a, \bigl\lbrack n, 1, 10\bigr\rbrack)

Out

\bigl\lbrack1, 1, 2, 3, 5, 8, 13, 21, 34, 55\bigr\rbrack

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