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 A076049 Numbers k such that the sum of the k-th triangular number and (k+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 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

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)