A076455 Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly two ways.

5, 57, 246, 710, 1635, 3255, 5852, 9756, 15345, 23045, 33330, 46722, 63791, 85155, 111480, 143480, 181917, 227601, 281390, 344190, 416955, 500687, 596436, 705300, 828425, 967005, 1122282, 1295546, 1488135, 1701435, 1936880, 2195952, 2480181

Offset

1,1

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

Formula

G.f.: x*(5 + 32*x + 11*x^2)/(1 - x)^5.

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

Maple

seq(1/2*n*(n+1)*(4*n^2+2*n-1), n=1..40);

Mathematica

CoefficientList[Series[(5 + 32 x + 11 x^2)/(1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)

Prog

(Magma) [n*(n+1)*(4*n^2+2*n-1)/2: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013

Crossrefs

Cf. A002417, A076454-A076459.

Sequence in context: A363059 A163793 A226425 * A196650 A197454 A196340

Adjacent sequences: A076452 A076453 A076454 * A076456 A076457 A076458

Keyword

nonn,easy

Author

Floor van Lamoen, Oct 13 2002

Status

approved