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 A228888 a(n) = binomial(3*n + 2, 3). 6
 10, 56, 165, 364, 680, 1140, 1771, 2600, 3654, 4960, 6545, 8436, 10660, 13244, 16215, 19600, 23426, 27720, 32509, 37820, 43680, 50116, 57155, 64824, 73150, 82160, 91881, 102340, 113564, 125580, 138415, 152096, 166650, 182104, 198485, 215820, 234136, 253460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA a(n) = binomial(3*n + 2, 3) = 1/6*(3*n)*(3*n + 1)*(3*n + 2). a(-n) = - A006566(n). a(n) = 1/6*A228889(n). G.f.: (10*x + 16*x^2 + x^3)/(1 - x)^4 = 10*x + 56*x^2 + 165*x^3 + .... Sum {n >= 1} 1/a(n) = 9/2 - 3/2*log(3) - 1/2*sqrt(3)*Pi. Sum {n >= 1} (-1)^n/a(n) = 9/2 - 4*log(2) - 1/3*sqrt(3)*Pi. EXAMPLE From Bruno Berselli, Jun 26 2018: (Start) Including 0, row sums of the triangle: | 0| .................................................................. 0 | 1| 2 3 4 ..................................................... 10 | 5| 6 7 8 9 10 11 ......................................... 56 |12| 13 14 15 16 17 18 19 20 21 ............................ 165 |22| 23 24 25 26 27 28 29 30 31 32 33 34 ................ 364 |35| 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 .... 680 ... in the first column of which we have the pentagonal numbers (A000326). (End) MAPLE seq(binomial(3*n+2, 3), n = 1..38); MATHEMATICA Table[(Binomial[3 n + 2, 3]), {n, 1, 40}] (* Vincenzo Librandi, Sep 09 2013 *) PROG (Magma) [Binomial(3*n + 2, 3): n in [1..40]]; // Vincenzo Librandi, Sep 09 2013 CROSSREFS Cf. A006566 (binomial(3*n,3)) and A228887 (binomial(3*n + 1,3)). Cf. A228889. Similar sequences are listed in A316224. Sequence in context: A000814 A202071 A281207 * A137931 A053493 A198833 Adjacent sequences: A228885 A228886 A228887 * A228889 A228890 A228891 KEYWORD nonn,easy AUTHOR Peter Bala, Sep 09 2013 STATUS approved

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Last modified May 28 04:05 EDT 2023. Contains 362992 sequences. (Running on oeis4.)