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

Author

Max Alekseyev, Sep 26 2013

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A045949.

Programs

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 ) }

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