A259907 Fifth differences of 7th powers (A001015).

1, 123, 1557, 6719, 16800, 31920, 52080, 77280, 107520, 142800, 183120, 228480, 278880, 334320, 394800, 460320, 530880, 606480, 687120, 772800, 863520, 959280, 1060080, 1165920, 1276800, 1392720, 1513680, 1639680, 1770720, 1906800, 2047920, 2194080, 2345280, 2501520, 2662800

Offset: 0

Author

Kolosov Petro, Jul 07 2015

Keywords

• nonn
• easy

Examples

			1 128 2187 16384 78125 279936 823543 2097152 4782969 (seventh powers)
1 127 2059 14197 61741 201811 543607 1273609 2685817 (first differences)
1 126 1932 12138 47544 140070 341796  730002 1412208 (second differences)
1 125 1806 10206 35406  92526 201726  388206  682206 (third differences)
1 124 1681  8400 25200  57120 109200  186480  294000 (fourth differences)
1 123 1557  6719 16800  31920  52080   77280  107520 (here)
		

References

• John H. Conway and Richard K. Guy, The Book of Numbers. New York: Springer-Verlag, pp. 30-32, 1996.
• Kiran Parulekar. Amazing Properties of Squares and Their Calculations. Kiran Anil Parulekar, 2012.
• Bag, Amulya Kumar (1966). "Binomial theorem in ancient India". Indian J. History Sci 1 (1): 68-74.
• Ronald Graham and Donald Knuth, Patashnik, Oren (1994). "(5) Binomial Coefficients". Concrete Mathematics (2nd ed.). Addison Wesley. pp. 153-256.

Links

• R. J. Mathar, Table of n, a(n) for n = 0..79
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001015, A022523, A255177, A255181.

Programs

Magma

[1,123,1557,6719] cat [840*(3*n^2-9*n+8): n in [4..40]]; // Bruno Berselli, Jul 16 2015

Mathematica

Join[{1, 123, 1557, 6719}, Table[840 (3 n^2 - 9 n + 8), {n, 4, 40}]]

Sage

[1,123,1557,6719]+[840*(3*n^2-9*n+8) for n in (4..40)] # Bruno Berselli, Jul 16 2015

Formula

G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^3.

a(n) = 840*(3*n^2 - 9*n + 8) for n>3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6. - Vincenzo Librandi, Jul 08 2015

Extensions

Edited by Editors of the OEIS, Jul 16 2015