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A076049 Numbers n such that sum of n-th triangular number and (n+2)-nd triangular number is a triangular number. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If c(n) are the entries in A069017, a is a(n) and T(a)=a*(a+1)/2 then T(a)+T(a+2)=c(n+1)

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) be the entries in A001109. 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.: A(x)=x*(3+5x-x^2-x^3)/((1-x)*(1-6x^2+x^4)). Closed form: a(n)=-3+(1/8)*(-1^n)((7+5sqrt(2))*(-1-sqrt(2))^n +(7-5*sqrt(2))*(-1+sqrt(2))^n-(1+sqrt(2))^n-(1-sqrt(2))^n)

CROSSREFS

Cf. 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

STATUS

approved

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Last modified February 24 11:12 EST 2018. Contains 299603 sequences. (Running on oeis4.)