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A259907 Fifth differences of 7th powers (A001015). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

EXAMPLE

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)

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A001015, A022523, A255177, A255181.

Sequence in context: A265983 A103504 A324627 * A115983 A202132 A167231

Adjacent sequences:  A259904 A259905 A259906 * A259908 A259909 A259910

KEYWORD

nonn,easy

AUTHOR

Kolosov Petro, Jul 07 2015

EXTENSIONS

Edited by Editors of the OEIS, Jul 16 2015

STATUS

approved

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Last modified September 25 12:38 EDT 2021. Contains 347654 sequences. (Running on oeis4.)