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A229620
Incorrect version of A045949.
0
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
V. Zhuravlev and P. Samovol, Mathematical enigmas of king Solomon's stamp, Kvant 1 (2012), 40-43. (in Russian)
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
KEYWORD
nonn,easy
AUTHOR
Max Alekseyev, Sep 26 2013
STATUS
approved