A076049 Numbers k such that the sum of the k-th triangular number and (k+2)-nd triangular number is a triangular number.

0, 3, 8, 25, 54, 153, 322, 899, 1884, 5247, 10988, 30589, 64050, 178293, 373318, 1039175, 2175864, 6056763, 12681872, 35301409, 73915374, 205751697, 430810378, 1199208779, 2510946900, 6989500983, 14634871028, 40737797125

Offset

1,2

Comments

T(a(n)) + T(a(n)+2) = A069017(n+1) where T(k) = k*(k+1)/2.

Links

Table of n, a(n) for n=1..28.

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

Formula

Let b(n) = A001109(n). Then we have a pair of recursion formulas:

a(2n+2) = 2*a(2n+1) - a(2n) + 2*b(n+1);

a(2n+3) = 2*a(2n+2) - a(2n+1) + 2*b(n+2).

G.f.: x*(3 + 5*x - x^2 - x^3)/((1-x)*(1 - 6*x^2 + x^4)).

a(n) = -3 + (1/8)*(-1^n)((7 + 5*sqrt(2))*(-1 - sqrt(2))^n + (7 - 5*sqrt(2))*(-1 + sqrt(2))^n - (1 + sqrt(2))^n - (1 - sqrt(2))^n).

Crossrefs

Cf. A000217, A001109, A069017.

Sequence in context: A220486 A180380 A057420 * A026970 A026980 A026955

Adjacent sequences: A076046 A076047 A076048 * A076050 A076051 A076052

Keyword

easy,nonn

Author

Bruce Corrigan (scentman(AT)myfamily.com), Oct 29 2002

Extensions

Edited by Jon E. Schoenfield, Sep 02 2019

Status

approved