

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
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OFFSET

0,3


COMMENTS

Partial sums give the generalized 18gonal numbers (A274979).
a(n) is also the length of the nth line segment of the rectangular spiral whose vertices are the generalized 18gonal 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(n2)  a(n4) 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 kgonal 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



