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 A082660 Number of ways n can be expressed as the sum of a square and a triangular number. 5
 1, 1, 1, 1, 1, 1, 2, 0, 0, 3, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 0, 0, 1, 1, 4, 0, 1, 2, 0, 1, 0, 1, 2, 3, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 0, 0, 3, 1, 1, 2, 0, 0, 4, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 3, 0, 1, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS It is assumed here that 0 is a square but not a triangular number. - Amiram Eldar, Dec 08 2019 The greedy inverse (positions of the first occurrence of n) is 1, 7, 10, 37, 136, 235, 1225, 631, 2116, 4789, 11026, 3997, 148240, 19045, 20827, 25876, ... - R. J. Mathar, Apr 28 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE a(631) = 8 because: 1. 631 = 6 + 625 2. 631 = 55 + 576 3. 631 = 190 + 441 4. 631 = 231 + 400 5. 631 = 406 + 225 6. 631 = 435 + 196 7. 631 = 595 + 36 8. 631 = 630 + 1 MAPLE A082660 := proc(n)     local a, tidx, t;     a := 0 ;     for tidx from 1 do         t := A000217(tidx) ;         if t > n then             break;         end if;         if issqr(n-t) then             a := a+1 ;         end if;     end do:     a ; end proc: # R. J. Mathar, Apr 28 2020 MATHEMATICA a[n_] := Length @ Solve[x^2 + y (y + 1)/2 == n && x >= 0 && y > 0, {x, y}, Integers]; Array[a, 100] (* Amiram Eldar, Dec 08 2019 *) CROSSREFS Cf. A000217, A000290, A082657, A082658, A082659. Sequence in context: A263414 A162934 A303908 * A134673 A131636 A188023 Adjacent sequences:  A082657 A082658 A082659 * A082661 A082662 A082663 KEYWORD nonn AUTHOR Jason Earls, May 17 2003 STATUS approved

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Last modified January 25 21:23 EST 2021. Contains 340427 sequences. (Running on oeis4.)