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A317315 Multiples of 15 and odd numbers interleaved. 4
0, 1, 15, 3, 30, 5, 45, 7, 60, 9, 75, 11, 90, 13, 105, 15, 120, 17, 135, 19, 150, 21, 165, 23, 180, 25, 195, 27, 210, 29, 225, 31, 240, 33, 255, 35, 270, 37, 285, 39, 300, 41, 315, 43, 330, 45, 345, 47, 360, 49, 375, 51, 390, 53, 405, 55, 420, 57, 435, 59, 450, 61, 465, 63, 480, 65, 495, 67, 510, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 19-gonal numbers (A303813).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 19-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) = 15*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 15*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 + 15*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008597 and A005408 interleaved.

Column 15 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. A303813.

Sequence in context: A248129 A256527 A040219 * A330361 A291157 A040216

Adjacent sequences:  A317312 A317313 A317314 * A317316 A317317 A317318

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)