A076460 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly one way.
1, 103, 1130, 6070, 22355, 64981, 160468, 351660, 703365, 1308835, 2297086, 3841058, 6166615, 9562385, 14390440, 21097816, 30228873, 42438495, 58506130, 79350670, 106046171, 139838413, 182162300, 234660100, 299200525, 377898651, 473136678, 587585530, 724227295
Offset: 1
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 (7,-21,35,-35,21,-7,1).
Programs
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Magma
[n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
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Maple
seq(1/6*n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1),n=1..30);
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Mathematica
CoefficientList[Series[(1 + 96 x + 430 x^2 + 288 x^3 + 25 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,103,1130,6070,22355,64981,160468},30] (* Harvey P. Dale, Jul 04 2025 *)
Formula
a(n) = n*(n+1)*(7*n^4+2*n^3-6*n^2-n+1)/6.
G.f.: x*(1+96*x+430*x^2+288*x^3+25*x^4)/(1-x)^7.
Extensions
More terms from Vincenzo Librandi, Dec 30 2013