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 A027474 a(n) = 7^(n-2) * C(n,2). 9
 1, 21, 294, 3430, 36015, 352947, 3294172, 29647548, 259416045, 2219448385, 18643366434, 154231485954, 1259557135291, 10173346092735, 81386768741880, 645668365352248, 5084638377148953, 39779817891812397, 309398583602985310 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS 7th binomial transform of (0,0,1,0,0,0,........). Starting at 1, the three-fold convolution of A000420 (powers of 7). - Paul Barry, Mar 08 2003 Number of n-permutations (n=3) of 8 objects r, q, u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(3)=21 because we have : uur, uuq, uuw, uuv, uuz, uux, uuy, uru, uqu, uwu, uvu, uzu, uxu, uyu, ruu, quu, wuu, vuu, zuu, xuu, yuu. - Zerinvary Lajos, Jun 12 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..400 Index entries for linear recurrences with constant coefficients, signature (21,-147,343). FORMULA G.f.: x^2 / (1-7x)^3. Recurrence: a(n) = 21a(n-1) - 147a(n-2) + 343a(n-3), a(0) = a(1) = 0, a(2) = 1. - Paul Barry, Mar 08 2003 Numerators of sequence a[ 3, n ] in (a[ i, j ])^3 where a[ i, j ] = Binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i. MAPLE seq(binomial(n, 2)*7^(n-2), n=2..30); # Zerinvary Lajos, Jun 12 2008 MATHEMATICA Table[7^(n-2) Binomial[n, 2], {n, 2, 20}] (* Harvey P. Dale, Sep 25 2011 *) PROG (Sage) [lucas_number2(n, 7, 0)*binomial(n, 2)/7^2 for n in range(2, 21)] # Zerinvary Lajos, Mar 13 2009 (MAGMA) [7^(n-2)* Binomial(n, 2): n in [2..20]]; /* Vincenzo Librandi, Oct 12 2011 */ (PARI) a(n)=7^(n-2)*n*(n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Third column of A027466. Cf. A081136, A081138. Sequence in context: A025962 A181381 A081137 * A021864 A020570 A025940 Adjacent sequences:  A027471 A027472 A027473 * A027475 A027476 A027477 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Ralf Stephan, Dec 30 2004 STATUS approved

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Last modified August 3 11:54 EDT 2020. Contains 336198 sequences. (Running on oeis4.)