A168574 a(n) = (4*n + 3)*(1 + 2*n^2)/3.

1, 7, 33, 95, 209, 391, 657, 1023, 1505, 2119, 2881, 3807, 4913, 6215, 7729, 9471, 11457, 13703, 16225, 19039, 22161, 25607, 29393, 33535, 38049, 42951, 48257, 53983, 60145, 66759, 73841, 81407, 89473, 98055, 107169, 116831, 127057, 137863, 149265, 161279

Offset

0,2

Comments

Binomial transform of quasi-finite sequence 1, 6, 20, 16, 0, 0, ... (0 continued).

a(n+1) is the sum of the first and last number at the bottom (2nd row) of each block in A172002, 3+4, 13+20, 39+56, ...

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 16.

a(n) = A168582(2*n+1) .

a(n+1) = A166911(n) + A002492(n+1).

G.f.: (1 + 3*x + 11*x^2 + x^3)/(1 - x)^4.

E.g.f.: (1/3)*(3 + 18*x + 30*x^2 + 8*x^3)*exp(x). - G. C. Greubel, Jul 26 2016

Mathematica

Table[ (4*n+3)*(1+2*n^2)/3 , {n, 0, 25}] (* G. C. Greubel, Jul 26 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 7, 33, 95}, 40] (* Harvey P. Dale, May 16 2019 *)

Prog

(Magma) [(4*n+3)*(1+2*n^2)/3 : n in [0..40]]; // Vincenzo Librandi, Aug 06 2011
(PARI) a(n)=(4*n+3)*(1+2*n^2)/3 \\ Charles R Greathouse IV, Jul 26 2016

Crossrefs

Cf. A168547, A168234.

Sequence in context: A060745 A275163 A051895 * A212106 A370214 A362300

Adjacent sequences: A168571 A168572 A168573 * A168575 A168576 A168577

Keyword

nonn,easy

Author

Paul Curtz, Nov 30 2009

Extensions

Edited and extended by R. J. Mathar, Mar 25 2010

Status

approved