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A317314 Multiples of 14 and odd numbers interleaved. 4
0, 1, 14, 3, 28, 5, 42, 7, 56, 9, 70, 11, 84, 13, 98, 15, 112, 17, 126, 19, 140, 21, 154, 23, 168, 25, 182, 27, 196, 29, 210, 31, 224, 33, 238, 35, 252, 37, 266, 39, 280, 41, 294, 43, 308, 45, 322, 47, 336, 49, 350, 51, 364, 53, 378, 55, 392, 57, 406, 59, 420, 61, 434, 63, 448, 65, 462, 67, 476, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 18-gonal numbers (A274979).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 18-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) = 14*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 14*x + x^2) / ((1 - x)^2*(1 + x)^2).

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

(End)

a(n) = 4*n + 3*n*(-1)^n. - Wesley Ivan Hurt, Nov 25 2021

MATHEMATICA

Table[4 n + 3 n (-1)^n, {n, 0, 80}] (* Wesley Ivan Hurt, Nov 25 2021 *)

PROG

(PARI) a(n) = if(n%2==0, return(14*n/2), return(n)) \\ Felix Fröhlich, Jul 26 2018

(PARI) concat(0, Vec(x*(1 + 14*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008596 and A005408 interleaved.

Column 14 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), A317311 (k=15), A317312 (k=16), A317313 (k=17).

Cf. A274979.

Sequence in context: A088576 A204159 A040190 * A163647 A060782 A182431

Adjacent sequences: A317311 A317312 A317313 * A317315 A317316 A317317

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)