A229620 Incorrect version of A045949.

0, 6, 38, 116, 256, 478, 798, 1236, 1808, 2534, 3430, 4516, 5808, 7326, 9086, 11108, 13408, 16006, 18918, 22164, 25760, 29726, 34078, 38836, 44016, 49638, 55718, 62276, 69328, 76894, 84990, 93636, 102848, 112646, 123046, 134068, 145728, 158046, 171038, 184724, 199120, 214246, 230118, 246756, 264176, 282398, 301438, 321316, 342048, 363654

Offset

0,2

Comments

Arises from the formula in Problem 11 of Zhuravlev and Samovol (2012) paper, which incorrectly claims it to produce sequence A045949. Terms a(n) for n<=3 match those of A045949 but afterwards the two sequences diverge. Nevertheless these sequences satisfy the same linear recurrent relation.

Links

Table of n, a(n) for n=0..49.

V. Zhuravlev and P. Samovol, Mathematical enigmas of king Solomon's stamp, Kvant 1 (2012), 40-43. (in Russian)

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

For even n, a(n) = n*(6*n^2+9*n-4)/2; for odd n, a(n) = (n+1)*(6*n^2+3*n+1)/2 - 4*n.

For n>=4, a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-2) + 3*a(n-3) - a(n-4).

a(n) = (1-(-1)^n-8*n+18*n^2+12*n^3)/4. G.f.: -2*x*(2*x+1)*(x^2-4*x-3) / ((x-1)^4*(x+1)). - Colin Barker, Sep 29 2013

E.g.f.: (x*(11 + 27*x + 6*x^2)*cosh(x) + (1 + 11*x + 27*x^2 + 6*x^3)*sinh(x))/2. - Stefano Spezia, Mar 20 2022

Prog

(PARI) { a(n) = if(n%2, (n+1)*(6*n^2+3*n+1)/2- 4*n, n*(6*n^2+9*n-4)/2 ) }

Crossrefs

Cf. A045949.

Sequence in context: A352305 A060454 A060452 * A045949 A189492 A281803

Adjacent sequences: A229617 A229618 A229619 * A229621 A229622 A229623

Keyword

nonn,easy

Author

Max Alekseyev, Sep 26 2013

Status

approved