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A317321 Multiples of 21 and odd numbers interleaved. 4
0, 1, 21, 3, 42, 5, 63, 7, 84, 9, 105, 11, 126, 13, 147, 15, 168, 17, 189, 19, 210, 21, 231, 23, 252, 25, 273, 27, 294, 29, 315, 31, 336, 33, 357, 35, 378, 37, 399, 39, 420, 41, 441, 43, 462, 45, 483, 47, 504, 49, 525, 51, 546, 53, 567, 55, 588, 57, 609, 59, 630, 61, 651, 63, 672, 65, 693, 67, 714, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 25-gonal numbers (A303304).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 25-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) = 21*n, a(2n+1) = 2*n + 1.

PROG

(PARI) concat(0, Vec(x*(1 + 21*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008603 and A005408 interleaved.

Column 21 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. A303304.

Sequence in context: A035419 A218249 A040433 * A080472 A118389 A077690

Adjacent sequences:  A317318 A317319 A317320 * A317322 A317323 A317324

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified October 15 03:16 EDT 2019. Contains 328025 sequences. (Running on oeis4.)