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 A131692 Sum of all n-digit Motzkin numbers. 0
 17, 72, 1285, 7986, 57346, 1277673, 8893161, 69051303, 543310782, 13365890713, 98677591278, 801766063038, 6557147147602, 53936034122790, 1399387730108461, 10689672477266256, 89312948959952446, 748842727830680421, 6298761061668331791, 53135898490140592293 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 23 14:31 EDT 2024. Contains 373651 sequences. (Running on oeis4.)