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A317316 Multiples of 16 and odd numbers interleaved. 4
0, 1, 16, 3, 32, 5, 48, 7, 64, 9, 80, 11, 96, 13, 112, 15, 128, 17, 144, 19, 160, 21, 176, 23, 192, 25, 208, 27, 224, 29, 240, 31, 256, 33, 272, 35, 288, 37, 304, 39, 320, 41, 336, 43, 352, 45, 368, 47, 384, 49, 400, 51, 416, 53, 432, 55, 448, 57, 464, 59, 480, 61, 496, 63, 512, 65, 528, 67, 544, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 20-gonal numbers (A218864).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 20-gonal numbers.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

a(2n) = 16*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 16*x + x^2) / ((1 - x)^2*(1 + x)^2).

a(n) = 2*a(n-2) - a(n-4) for n>3.

(End)

PROG

(PARI) concat(0, Vec(x*(1 + 16*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008598 and A005408 interleaved.

Column 16 of A195151.

Sequences whose partial sums give the generalized k-gonal numbers: A026741 (k=5), A001477 (k=6), zero together with A080512 (k=7), A022998 (k=8), A195140 (k=9), zero together with A165998 (k=10), A195159 (k=11), A195161 (k=12), A195312 k=13), A195817 (k=14).

Cf. A218864.

Sequence in context: A139722 A070582 A070569 * A084473 A343051 A040246

Adjacent sequences:  A317313 A317314 A317315 * A317317 A317318 A317319

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)