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 A247247 Triangular numbers that are the sum of 2 consecutive terms of A130518. 1
 0, 1, 3, 21, 120, 300, 2080, 11781, 29403, 203841, 1154440, 2881200, 19974360, 113123361, 282328203, 1957283461, 11084934960, 27665282700, 191793804840, 1086210502741, 2710915376403, 18793835590881, 106437544333680, 265642041604800, 1841604094101520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS What will be the distribution of these triangular numbers? Will they mostly be multiples of three? From Hiroaki Yamanouchi, Dec 04 2014: (Start) a(n) is some nonnegative x in the integer solutions (x, y) of (1) (6*x + 3)^2 - 6*(6*y + 4)^2 = -15, (2) (6*x + 3)^2 - 6*(6*y + 8)^2 = -15 or (3) (2*x + 1)^2 - 6*(2*y + 2)^2 = 1. (End) LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..1000 FORMULA Empirical G.f.: x^2*(x+1)*(x^4+2*x^3+19*x^2+2*x+1)/((1-x)*(x^2+x+1)*(x^6-98*x^3+1)). - Robert Israel, Nov 30 2014 EXAMPLE A130518(8)+A130518(9) = 9+12 = 21 = A000217(6), so 21 is in the sequence. MAPLE f:= proc(n) local x; x:= ceil((n^2+2*n)/3); if issqr(1+8*x) then x else NULL fi end proc: seq(f(n), n=0..10^6); # Robert Israel, Nov 30 2014 MATHEMATICA a247247[n_Integer] := Module[{a130518, a000217, s}, a130518[m_] := Table[i, {i, 0, m}, {3}] // Flatten // Accumulate; a000217[m_] := Accumulate[Range[m]]; s[m_] := a130518[m] + Most@PrependTo[a130518[m], 0] // DeleteDuplicates; Intersection[s[n], a000217[n]]]; a247247[50000000] (* Michael De Vlieger, Nov 30 2014 after Jean-François Alcover at A130518 and Harvey P. Dale at A000217 *) CROSSREFS Cf. A000217, A130518. Sequence in context: A283421 A117512 A068127 * A322185 A171137 A144884 Adjacent sequences: A247244 A247245 A247246 * A247248 A247249 A247250 KEYWORD nonn AUTHOR J. M. Bergot, Nov 28 2014 EXTENSIONS a(7)-a(13) from Michel Marcus, Nov 28 2014 a(14)-a(24) from Michael De Vlieger, Nov 30 2014 a(25) from Hiroaki Yamanouchi, Dec 04 2014 STATUS approved

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Last modified November 29 22:05 EST 2023. Contains 367452 sequences. (Running on oeis4.)