# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001753 Showing 1-1 of 1 %I A001753 #46 Jan 18 2024 09:52:25 %S A001753 1,5,16,40,86,166,296,496,791,1211,1792,2576,3612,4956,6672,8832, %T A001753 11517,14817,18832,23672,29458,36322,44408,53872,64883,77623,92288, %U A001753 109088,128248,150008,174624,202368,233529 %N A001753 Expansion of 1/((1+x)*(1-x)^6). %C A001753 Number of symmetric nonnegative integer 5 X 5 matrices with sum of elements equal to 4*n under action of dihedral group D_4. %C A001753 a(n) = A108561(n+6,n) for n>0. - _Reinhard Zumkeller_, Jun 10 2005 %H A001753 Vincenzo Librandi, Table of n, a(n) for n = 0..10000 %H A001753 Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1) %F A001753 a(n) = Sum{k=0..n} (-1)^(n-k)*binomial(k+5, 5); a(n) = (4*n^5 + 70*n^4 + 460*n^3 + 1400*n^2 + 1936*n + 945)/960 + (-1)^n/64. - _Paul Barry_, Jul 01 2003 %F A001753 a(n) = a(n-2) + (n*(n + 1)*(n + 2)*(n - 1))/24, a(1) = 0, a(2) = 1; (15*(-1)^n - 15*(-1)^(2*n) + 96*n - 160*(-1)^(2*n)*n + 200*n^2 - 200*(-1)^(2*n)*n^2 + 140*n^3 - 80*(-1)^(2*n)*n^3 + 40*n^4 - 10*(-1)^(2*n)*n^4 + 4*n^5)/960. - Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004 %F A001753 a(n) + a(n+1) = A000389(n+6). - _R. J. Mathar_, Mar 14 2011 %e A001753 There are 5 symmetric nonnegative integer 5 X 5 matrices with sum of elements equal to 4 under action of D_4: %e A001753 [1 0 0 0 1] [0 0 1 0 0] [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0] %e A001753 [0 0 0 0 0] [0 0 0 0 0] [0 1 0 1 0] [0 0 1 0 0] [0 0 0 0 0] %e A001753 [0 0 0 0 0] [1 0 0 0 1] [0 0 0 0 0] [0 1 0 1 0] [0 0 4 0 0] %e A001753 [0 0 0 0 0] [0 0 0 0 0] [0 1 0 1 0] [0 0 1 0 0] [0 0 0 0 0] %e A001753 [1 0 0 0 1] [0 0 1 0 0] [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0]. %t A001753 CoefficientList[Series[1/((1+x)*(1-x)^6), {x, 0, 50}], x] (* _G. C. Greubel_, Nov 22 2017 *) %t A001753 LinearRecurrence[{5,-9,5,5,-9,5,-1},{1,5,16,40,86,166,296},40] (* _Harvey P. Dale_, Jun 05 2021 *) %o A001753 (Magma) [(4*n^5+70*n^4+460*n^3+1400*n^2+1936*n+945)/960+(-1)^n/64: n in [0..40]]; // _Vincenzo Librandi_, Aug 15 2011 %o A001753 (PARI) a(n)=(4*n^5+70*n^4+460*n^3+1400*n^2+1936*n)\/960+1 \\ _Charles R Greathouse IV_, Apr 17 2012 %Y A001753 Cf. A000217, A002620, A008804, A038163, A054343, A001769 (partial sums), A001752 (first differences), A169793 (binomial transf). %K A001753 nonn,easy %O A001753 0,2 %A A001753 _N. J. A. Sloane_ %E A001753 Comment and example from _Vladeta Jovovic_, May 14 2000 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE