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A317313 Multiples of 13 and odd numbers interleaved. 5
0, 1, 13, 3, 26, 5, 39, 7, 52, 9, 65, 11, 78, 13, 91, 15, 104, 17, 117, 19, 130, 21, 143, 23, 156, 25, 169, 27, 182, 29, 195, 31, 208, 33, 221, 35, 234, 37, 247, 39, 260, 41, 273, 43, 286, 45, 299, 47, 312, 49, 325, 51, 338, 53, 351, 55, 364, 57, 377, 59, 390, 61, 403, 63, 416, 65, 429, 67, 442, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums give the generalized 17-gonal numbers (A303305).

More generally, the partial sums of the sequence formed by the multiples of m and the odd numbers interleaved, give the generalized k-gonal numbers, with m >= 1 and k = m + 4.

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 17-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) = 13*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 13*x + x^2) / ((1 - x)^2*(1 + x)^2).

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

(End)

MATHEMATICA

Table[{13n, 2n + 1}, {n, 0, 35}] // Flatten (* or *)

CoefficientList[Series[(x^3 + 13 x^2 + x)/(x^2 - 1)^2, {x, 0, 69}], x] (* or *)

LinearRecurrence[{0, 2, 0, -1}, {0, 1, 13, 3}, 70] (* Robert G. Wilson v, Jul 26 2018 *)

PROG

(PARI) a(n) = if(n%2==0, return((n/2)*13), return(n)) \\ Felix Fröhlich, Jul 26 2018

(PARI) concat(0, Vec(x*(1 + 13*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

CROSSREFS

Cf. A008595 and A005408 interleaved.

Column 13 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).

Cf. A303305.

Sequence in context: A264971 A107806 A138965 * A170922 A005602 A272175

Adjacent sequences:  A317310 A317311 A317312 * A317314 A317315 A317316

KEYWORD

nonn,easy,mult

AUTHOR

Omar E. Pol, Jul 25 2018

STATUS

approved

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)