A131478 a(n) = ceiling(n^4/4).

0, 1, 4, 21, 64, 157, 324, 601, 1024, 1641, 2500, 3661, 5184, 7141, 9604, 12657, 16384, 20881, 26244, 32581, 40000, 48621, 58564, 69961, 82944, 97657, 114244, 132861, 153664, 176821, 202500, 230881, 262144, 296481, 334084, 375157, 419904, 468541, 521284

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

Formula

From R. J. Mathar, Dec 19 2008: (Start)

G.f.: x*(1 + 10*x^2 + x^4)/((1 - x)^5*(1 + x)).

a(n) + a(n+1) = A058919(n+1). (End)

a(n) = floor(n^4/4 + 3/4). - Bruno Berselli, Dec 21 2017

E.g.f.: (x*(x^3 + 6*x^2 + 7*x + 1)*cosh(x) + (x^4 + 6*x^3 + 7*x^2 + x + 3)*sinh(x))/4. - Stefano Spezia, Feb 18 2023

Mathematica

Ceiling[Range[0, 40]^4/4] (* Harvey P. Dale, May 17 2019 *)
CoefficientList[Series[(x(x^3 + 6x^2 + 7x + 1)Cosh[x]+ (x^4 + 6x^3 + 7x^2 + x + 3)Sinh[x])/4, {x, 0, 35}], x]Table[n!, {n, 0, 35}] (* Stefano Spezia, Feb 19 2023 *)

Prog

(Magma) [Ceiling(n^4/4) : n in [0..50]]; // Vincenzo Librandi, Oct 01 2011
(PARI) vector(50, n, n--; ceil(n^4/4)) \\ Michel Marcus, Jun 16 2015
(Python)
def A131478(n): return n**4+3>>2 # Chai Wah Wu, Jan 30 2023

Crossrefs

Cf. A000982, A004526, A007590, A008619, A036487, A058919.

Cf. A131479.

Sequence in context: A332981 A135559 A254449 * A089893 A212246 A359065

Adjacent sequences: A131475 A131476 A131477 * A131479 A131480 A131481

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jul 27 2007

Status

approved