A131692 Sum of all n-digit Motzkin numbers.

17, 72, 1285, 7986, 57346, 1277673, 8893161, 69051303, 543310782, 13365890713, 98677591278, 801766063038, 6557147147602, 53936034122790, 1399387730108461, 10689672477266256, 89312948959952446, 748842727830680421, 6298761061668331791, 53135898490140592293

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Motzkin Number

Example

Sum of all 1-digit Motzkin numbers is 1 + 1 + 2 + 4 + 9 = 17.
Sum of all 2-digit Motzkin numbers is 21 + 52 = 72.
Sum of all 3-digit Motzkin numbers is 127 + 323 + 835 = 1285.

Mathematica

digNum[n_] := Length @ IntegerDigits[n]; mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; digCount = 0; sum = 0; cumsum = {}; Do[m = mot[n]; If[digNum[m] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += m, {n, 0, 50}]; Differences[cumsum] (* Amiram Eldar, Nov 30 2019 *)

Crossrefs

Cf. A001006.

Sequence in context: A087514 A119625 A130748 * A157864 A229496 A268544

Adjacent sequences: A131689 A131690 A131691 * A131693 A131694 A131695

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Sep 15 2007

Extensions

More terms from Amiram Eldar, Nov 30 2019

Status

approved