A034706 Numbers which are sums of consecutive triangular numbers.
0, 1, 3, 4, 6, 9, 10, 15, 16, 19, 20, 21, 25, 28, 31, 34, 35, 36, 45, 46, 49, 52, 55, 56, 64, 66, 74, 78, 80, 81, 83, 84, 85, 91, 100, 105, 109, 110, 116, 119, 120, 121, 130, 136, 144, 145, 153, 155, 161, 164, 165, 166, 169, 171, 185, 190, 196, 199, 200, 202, 210
Offset: 1
Keywords
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- D. Subramaniam, E. Trevino, and P. Pollack, On sums of consecutive triangular numbers, INTEGERS 20A (2020) A15.
Crossrefs
Programs
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Haskell
-- import Data.Set (deleteFindMin, union, fromList); import Data.List (inits) a034706 n = a034706_list !! (n-1) a034706_list = f 0 (tail $ inits $ a000217_list) (fromList [0]) where f x vss'@(vs:vss) s | y < x = y : f x vss' s' | otherwise = f w vss (union s $ fromList $ scanl1 (+) ws) where ws@(w:_) = reverse vs (y, s') = deleteFindMin s -- Reinhard Zumkeller, May 12 2015 -
Maple
isA034706 := proc(n) local a,b; for a from 0 do if a*(a+1)/2 > n then return false; end if; for b from a do tab := (1+b-a)*(a^2+b*a+a+b^2+2*b)/6 ; if tab = n then return true; elif tab > n then break; end if; end do: end do: end proc: for n from 0 to 100 do if isA034706(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Dec 14 2015
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Mathematica
M = 1000; (* to get all terms <= M *) nmax = (Sqrt[8 M + 1] - 1)/2 // Ceiling; Table[Sum[n(n+1)/2, {n, j, k}], {j, 0, nmax}, {k, j, nmax}] // Flatten // Union // Select[#, # <= M&]& (* Jean-François Alcover, Mar 10 2019 *)