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A317318 Multiples of 18 and odd numbers interleaved. 4
0, 1, 18, 3, 36, 5, 54, 7, 72, 9, 90, 11, 108, 13, 126, 15, 144, 17, 162, 19, 180, 21, 198, 23, 216, 25, 234, 27, 252, 29, 270, 31, 288, 33, 306, 35, 324, 37, 342, 39, 360, 41, 378, 43, 396, 45, 414, 47, 432, 49, 450, 51, 468, 53, 486, 55, 504, 57, 522, 59, 540, 61, 558, 63, 576, 65, 594, 67, 612, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 22-gonal numbers (A303299).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 22-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) = 18*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 18*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 + 18*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008600 and A005408 interleaved.

Column 18 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. A303299.

Sequence in context: A135216 A135252 A040317 * A321263 A040313 A051522

Adjacent sequences:  A317315 A317316 A317317 * A317319 A317320 A317321

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)