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A259181 a(n) = n*(n+1)*(n+2)*(n+3)*(2*n^2+6*n+7)/360. 4
0, 1, 9, 43, 147, 406, 966, 2058, 4026, 7359, 12727, 21021, 33397, 51324, 76636, 111588, 158916, 221901, 304437, 411103, 547239, 719026, 933570, 1198990, 1524510, 1920555, 2398851, 2972529, 3656233, 4466232, 5420536, 6539016, 7843528, 9358041, 11108769 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
After 0, second bisection of A129548.
This sequence is also the total number of squares of all sizes in i X i subsquares in an n X n grid, whereas A000330 simply gives the number of all sizes of squares in an n X n grid. See illustrations.
LINKS
FORMULA
a(n) = (1/6)*Sum_{i=0..n} (i+1)*(i+2)*(2*i+3)*(n-i)^2.
a(n) = Sum_{i=0..n} A000290(n-i)*A000330(i+1).
G.f.: x*(1 + x)^2 / (1 - x)^7. - Colin Barker, Nov 08 2015
a(n) = (A000539(n+1) - A000217(n+1))/30. - Yasser Arath Chavez Reyes, Feb 24 2024
EXAMPLE
a(0) = 0; a(1) = 1*1; a(2) = 4*1+1*5 = 9; a(3) = 9*1+4*5+1*14 = 43.
PROG
(PARI) vector(100, n, n--; n*(n+1)*(n+2)*(n+3)*(2*n^2+6*n+7)/360) \\ Altug Alkan, Nov 08 2015
(PARI) concat(0, Vec(-x*(x+1)^2 / (x-1)^7 + O(x^100))) \\ Colin Barker, Nov 08 2015
CROSSREFS
Cf. A060060: (1/6)*Sum_{i=0..n} (i+1)*(i+2)*(2*i+3)*i^2.
Sequence in context: A332373 A181945 A244869 * A330088 A281773 A220676
KEYWORD
nonn,easy
AUTHOR
Luce ETIENNE, Nov 08 2015
STATUS
approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)