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A317320 Multiples of 20 and odd numbers interleaved. 4
0, 1, 20, 3, 40, 5, 60, 7, 80, 9, 100, 11, 120, 13, 140, 15, 160, 17, 180, 19, 200, 21, 220, 23, 240, 25, 260, 27, 280, 29, 300, 31, 320, 33, 340, 35, 360, 37, 380, 39, 400, 41, 420, 43, 440, 45, 460, 47, 480, 49, 500, 51, 520, 53, 540, 55, 560, 57, 580, 59, 600, 61, 620, 63, 640, 65, 660, 67, 680, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 24-gonal numbers (A303814).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 24-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(n) = n, if n is odd.

a(n) = 10*n, if n is even.

a(2n) = 20*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 20*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[20*Range[0, nn], Range[1, 2*nn+1, 2]]] (* Harvey P. Dale, Feb 16 2020 *)

PROG

(PARI) concat(0, Vec(x*(1 + 20*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008602 and A005408 interleaved.

Column 20 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. A303814.

Sequence in context: A070645 A248136 A040392 * A327701 A337157 A040388

Adjacent sequences:  A317317 A317318 A317319 * A317321 A317322 A317323

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified July 31 04:58 EDT 2021. Contains 346367 sequences. (Running on oeis4.)