A133199 Sum of all n-digit cake numbers.

15, 240, 4780, 97055, 2025120, 43102338, 933680790, 20113923047, 433568150212, 9328838294868, 201092030447970, 4332220161894898, 93326831839333367, 2010735085618839810, 43319850539113451407, 933285813634428329651, 20107085833468562876519, 433194255274554129774434

Offset

1,1

Links

Table of n, a(n) for n=1..18.

E.W. Weisstein, Cylinder Cutting

Example

Sum of all 1-digit cake numbers is 1 + 2 + 4 + 8 = 15.
Sum of all 2-digit cake numbers is 15 + 26 + 42 + 64 + 93 = 240.
Sum of all 3-digit cake numbers is 130 + 176 + 232 + 299 + 378 + 470 + 576 + 697 + 834 + 988 = 4780.

Mathematica

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 *)

Crossrefs

Cf. A000125.

Sequence in context: A220821 A090411 A154806 * A059760 A059615 A215855

Adjacent sequences: A133196 A133197 A133198 * A133200 A133201 A133202

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Oct 10 2007

Extensions

More terms from Amiram Eldar, Nov 30 2019

Status

approved