A076465 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly n ways.

1, 571, 12938, 115270, 630755, 2543401, 8307796, 23249388, 57792165, 130790935, 274285726, 540036146, 1008233863, 1798831685, 3085968040, 5116005976, 8229746121, 12889413363, 19711057330, 29503047070, 43311380651, 62472570721, 88674907388, 124028940100

Offset

1,2

References

Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

a(n) = n*(n+1)*(6*n^6+12*n^5-5*n^4-16*n^3+5*n+1)/6.

G.f.: x*(1+562*x+7835*x^2+19300*x^3+11255*x^4+1354*x^5+13*x^6)/(1-x)^9.

a(1)=1, a(2)=571, a(3)=12938, a(4)=115270, a(5)=630755, a(6)=2543401, a(7)=8307796, a(8)=23249388, a(9)=57792165, a(n)=9*a(n-1)- 36*a(n-2)+ 84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Sep 05 2015

Maple

seq(1/6*n*(n+1)*(6*n^6+12*n^5-5*n^4-16*n^3+5*n+1), n=1..25);

Mathematica

CoefficientList[Series[(1 + 562 x + 7835 x^2 + 19300 x^3 + 11255 x^4 + 1354 x^5 + 13 x^6)/(1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 571, 12938, 115270, 630755, 2543401, 8307796, 23249388, 57792165}, 30] (* Harvey P. Dale, Sep 05 2015 *)

Prog

(Magma) [n*(n+1)*(6*n^6+12*n^5-5*n^4-16*n^3+5*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013

Crossrefs

Cf. A076389, A076459-A076464.

Sequence in context: A020381 A142767 A251384 * A144956 A178323 A049361

Adjacent sequences: A076462 A076463 A076464 * A076466 A076467 A076468

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 13 2002

Extensions

More terms from Vincenzo Librandi, Dec 30 2013

Status

approved