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A317319 Multiples of 19 and odd numbers interleaved. 4
0, 1, 19, 3, 38, 5, 57, 7, 76, 9, 95, 11, 114, 13, 133, 15, 152, 17, 171, 19, 190, 21, 209, 23, 228, 25, 247, 27, 266, 29, 285, 31, 304, 33, 323, 35, 342, 37, 361, 39, 380, 41, 399, 43, 418, 45, 437, 47, 456, 49, 475, 51, 494, 53, 513, 55, 532, 57, 551, 59, 570, 61, 589, 63, 608, 65, 627, 67, 646, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 23-gonal numbers (A303303).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 23-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) = 19*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 19*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 + 19*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008601 and A005408 interleaved.

Column 19 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. A303303.

Sequence in context: A040352 A040353 A128160 * A002206 A040349 A274249

Adjacent sequences:  A317316 A317317 A317318 * A317320 A317321 A317322

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified September 17 09:01 EDT 2019. Contains 327128 sequences. (Running on oeis4.)