A093917 a(n) = n^3+n for odd n, (n^3+n)*3/2 for even n: Row sums of A093915.

2, 15, 30, 102, 130, 333, 350, 780, 738, 1515, 1342, 2610, 2210, 4137, 3390, 6168, 4930, 8775, 6878, 12030, 9282, 16005, 12190, 20772, 15650, 26403, 19710, 32970, 24418, 40545, 29822, 49200, 35970, 59007, 42910, 70038, 50690, 82365, 59358

Offset: 1

Author

Amarnath Murthy, Apr 25 2004

Keywords

• nonn
• easy

Comments

Initially defined as sum of the n-th row of the triangle A093915, constructed by trial and error. Namely, this row should contain n consecutive integers [x,x+1,...,x+n-1], listed in A093915, and have its sum a(n) = n*x+n(n-1)/2 equal to the least possible strict (>1) multiple of the sum of the indices of these elements in A093915, which equals A006003(n) = (n^3+n)/2. For odd n, a(n) = 2 A006003(n) is obtained for x = A093916(n). For even n, the sum a(n) cannot equal 2 A006003(n), but it does equal 3 A006003(n) for x = A093916(n). Hence this simple explicit definition of a(n). - M. F. Hasler, Apr 04 2009

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A093915, A093916, A093918.

Formula

a(n) = n*A093916(n)+n(n-1)/2. - M. F. Hasler, Apr 04 2009

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

G.f.: x*(2+15*x+22*x^2+42*x^3+22*x^4+15*x^5+2*x^6) / ( (x-1)^4*(1+x)^4 ). - R. J. Mathar, Mar 21 2016

Extensions

More terms from Jorge Coveiro, Jul 25 2006

Edited by M. F. Hasler, Apr 04 2009