A098583 Expansion of (1+2*x+4*x^2+8*x^3+16*x^4)/(1-x-32*x^6).

1, 3, 7, 15, 31, 31, 63, 159, 383, 863, 1855, 2847, 4863, 9951, 22207, 49823, 109183, 200287, 355903, 674335, 1384959, 2979295, 6473151, 12882335, 24271231, 45849951, 90168639, 185506079, 392646911, 804881631, 1581561023, 3048759455

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,32).

Formula

a(n) = a(n-1) + 32*a(n-6).

a(n) = Sum_{k=0..n} binomial(n-k, floor(k/5)) * 2^k.

Mathematica

CoefficientList[Series[(1+2x+4x^2+8x^3+16x^4)/(1-x-32x^6), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 32}, {1, 3, 7, 15, 31, 31}, 40] (* Harvey P. Dale, May 02 2014 *)

Prog

(PARI) x='x+O('x^30); Vec((1+2*x+4*x^2+8*x^3+16*x^4)/(1-x-32*x^6)) \\ G. C. Greubel, Feb 03 2018
(Magma) I:=[1, 3, 7, 15, 31, 31]; [n le 6 select I[n] else Self(n-1) + 32*Self(n-6): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Crossrefs

Cf. A098582.

Sequence in context: A064084 A090633 A320024 * A275531 A275532 A212315

Adjacent sequences: A098580 A098581 A098582 * A098584 A098585 A098586

Keyword

easy,nonn

Author

Paul Barry, Sep 16 2004

Status

approved