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A317317 Multiples of 17 and odd numbers interleaved. 4
0, 1, 17, 3, 34, 5, 51, 7, 68, 9, 85, 11, 102, 13, 119, 15, 136, 17, 153, 19, 170, 21, 187, 23, 204, 25, 221, 27, 238, 29, 255, 31, 272, 33, 289, 35, 306, 37, 323, 39, 340, 41, 357, 43, 374, 45, 391, 47, 408, 49, 425, 51, 442, 53, 459, 55, 476, 57, 493, 59, 510, 61, 527, 63, 544, 65, 561, 67, 578, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 21-gonal numbers (A303298).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 21-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) = 17*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 17*x + x^2) / ((1 - x)^2*(1 + x)^2).

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

(End)

MATHEMATICA

With[{nn=40}, Riffle[17*Range[0, nn], 2*Range[0, nn]+1]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 17, 3}, 80] (* Harvey P. Dale, Jun 06 2020 *)

PROG

(PARI) concat(0, Vec(x*(1 + 17*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008599 and A005408 interleaved.

Column 17 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. A303298.

Sequence in context: A040282 A139728 A336485 * A212602 A174380 A040278

Adjacent sequences:  A317314 A317315 A317316 * A317318 A317319 A317320

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified June 23 17:39 EDT 2021. Contains 345402 sequences. (Running on oeis4.)