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%I #11 Nov 30 2019 09:13:43
%S 15,240,4780,97055,2025120,43102338,933680790,20113923047,
%T 433568150212,9328838294868,201092030447970,4332220161894898,
%U 93326831839333367,2010735085618839810,43319850539113451407,933285813634428329651,20107085833468562876519,433194255274554129774434
%N Sum of all n-digit cake numbers.
%H E.W. Weisstein, <a href="http://mathworld.wolfram.com/CylinderCutting.html">Cylinder Cutting</a>
%e Sum of all 1-digit cake numbers is 1 + 2 + 4 + 8 = 15.
%e Sum of all 2-digit cake numbers is 15 + 26 + 42 + 64 + 93 = 240.
%e Sum of all 3-digit cake numbers is 130 + 176 + 232 + 299 + 378 + 470 + 576 + 697 + 834 + 988 = 4780.
%t digNum[n_] := Length @ IntegerDigits[n]; cake[n_] := (n^3 + 5n + 6)/6; digCount = 0; sum = 0; cumsum = {}; Do[c = cake[n]; If[digNum[c] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += c, {n, 0, 10^6}]; Differences[cumsum] (* _Amiram Eldar_, Nov 30 2019 *)
%Y Cf. A000125.
%K nonn,base,less
%O 1,1
%A _Parthasarathy Nambi_, Oct 10 2007
%E More terms from _Amiram Eldar_, Nov 30 2019