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A195045 Concentric 13-gonal numbers. 8
0, 1, 13, 27, 52, 79, 117, 157, 208, 261, 325, 391, 468, 547, 637, 729, 832, 937, 1053, 1171, 1300, 1431, 1573, 1717, 1872, 2029, 2197, 2367, 2548, 2731, 2925, 3121, 3328, 3537, 3757, 3979, 4212, 4447, 4693, 4941, 5200, 5461, 5733, 6007, 6292, 6579, 6877, 7177, 7488, 7801, 8125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also concentric tridecagonal numbers or concentric triskaidecagonal numbers.

Partial sums of A175886. - Reinhard Zumkeller, Jan 07 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

a(n) = 13*n^2/4+9*((-1)^n-1)/8.

G.f.: -x*(1+11*x+x^2) / ( (1+x)*(x-1)^3 ). a(n)+a(n+1) = A069126(n+1). - R. J. Mathar, Sep 28 2011

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3. - Wesley Ivan Hurt, Nov 22 2015

MAPLE

A195045:=n->13*n^2/4+9*((-1)^n-1)/8: seq(A195045(n), n=0..70); # Wesley Ivan Hurt, Nov 22 2015

MATHEMATICA

Table[13 n^2/4 + 9 ((-1)^n - 1)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Nov 22 2015 *)

PROG

(MAGMA) [13*n^2/4+9*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011

(Haskell)

a195045 n = a195045_list !! n

a195045_list = scanl (+) 0 a175886_list

-- Reinhard Zumkeller, Jan 07 2012

(PARI) a(n)=13*n^2/4+9*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

(PARI) concat(0, Vec(-x*(1+11*x+x^2)/((1+x)*(x-1)^3) + O(x^50))) \\ Altug Alkan, Nov 22 2015

CROSSREFS

Column 13 of A195040.

Cf. A032527, A032528, A069126, A175886, A195043, A195046, A195143, A195145.

Sequence in context: A132755 A250667 A147450 * A098266 A041332 A041334

Adjacent sequences:  A195042 A195043 A195044 * A195046 A195047 A195048

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 27 2011

STATUS

approved

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Last modified March 30 04:51 EDT 2017. Contains 284296 sequences.