A132156 Sum of all n-digit Stern numbers.

13, 148, 1003, 16141, 117547, 917053, 15502289, 114274754, 909482399, 15471962269, 115061008452, 917885746619, 15675637954053, 116877859994048, 933643385166035, 15975162211603393, 119196492782053456, 952870691477908028, 16319572144410372393, 121792577413939691253

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Example

Sum of all 1-digit Stern numbers is 1 + 1 + 2 + 3 + 6 = 13.
Sum of all 2-digit Stern numbers is 11 + 20 + 40 + 77 = 148.
Sum of all 3-digit Stern numbers is 148 + 285 + 570 = 1003.

Mathematica

stern[1] = 1; stern[n_] := stern[n] = Sum[stern[k], {k, n - Ceiling[(Sqrt[8*n -7]-1)/2], n-1}]; digNum[n_] := Length @ IntegerDigits[n]; digCount = 0; sum = 0; cumsum = {}; Do[s = stern[n]; If[digNum[s] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += s, {n, 1, 25}]; Differences[cumsum] (* Amiram Eldar, Nov 30 2019 *)

Crossrefs

Cf. A005230.

Sequence in context: A016135 A332691 A210165 * A324356 A210158 A130611

Adjacent sequences: A132153 A132154 A132155 * A132157 A132158 A132159

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Nov 01 2007

Extensions

More terms from Amiram Eldar, Nov 30 2019

Status

approved