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A357178
First differences of cubes of triangular numbers.
1
0, 1, 26, 189, 784, 2375, 5886, 12691, 24704, 44469, 75250, 121121, 187056, 279019, 404054, 570375, 787456, 1066121, 1418634, 1858789, 2402000, 3065391, 3867886, 4830299, 5975424, 7328125, 8915426, 10766601, 12913264, 15389459, 18231750, 21479311, 25174016, 29360529
OFFSET
0,3
COMMENTS
Row sums of centered hexagonal numbers A003215 treated as a regular triangle.
FORMULA
a(n) = (n^3 + 3*n^5)/4.
G.f.: x*(1 + 20*x + 48*x^2 + 20*x^3 + x^4)/(1 - x)^6. - Stefano Spezia, Sep 19 2022
MATHEMATICA
a[n_] := (n^3 + 3*n^5)/4; Array[a, 35, 0] (* Amiram Eldar, Sep 18 2022 *)
PROG
(PARI) a(n) = n^3*(3*n^2+1)/4 \\ Charles R Greathouse IV, Sep 19 2022
CROSSREFS
Cf. A059827 (cubes of triangular numbers).
Cf. A000578 (for squares) and A168364 (for fourth powers) of triangular numbers.
Cf. A000217 (triangular numbers), A003215.
Sequence in context: A042312 A181342 A090960 * A262107 A245952 A056026
KEYWORD
nonn,easy
AUTHOR
Kelvin Voskuijl, Sep 16 2022
STATUS
approved