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A247817 Sum(4^k, k=2..n). 4
0, 16, 80, 336, 1360, 5456, 21840, 87376, 349520, 1398096, 5592400, 22369616, 89478480, 357913936, 1431655760, 5726623056, 22906492240, 91625968976, 366503875920, 1466015503696, 5864062014800, 23456248059216, 93824992236880, 375299968947536, 1501199875790160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (5,-4).

FORMULA

G.f.: 16*x^2/((1-x)*(1-4*x)).

a(n) = a(n-1) + 4^n = (4^(n+1) - 16)/3 = 5*a(n-1) - 4*a(n-2).

a(n) = A080674(n) - 4. - Michel Marcus, Sep 25 2014

MATHEMATICA

RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 4^n}, a, {n, 30}] (* or *) CoefficientList[Series[16 x / ((1 - x) (1 - 4 x)), {x, 0, 40}], x]

PROG

(MAGMA) [0] cat [&+[4^k: k in [2..n]]: n in [2..30]]; /* or */ [(4^(n+1)-16)/3: n in [1..30]];

(PARI) a(n) = sum(k=2, n, 4^k); \\ Michel Marcus, Sep 25 2014

CROSSREFS

Cf. Sum(h^k,k=2..n): A028329 (h=2), A168569 (h=3), this sequence (h=4), A168571 (h=5), A247840 (h=6), A168572 (h=7), A247841 (h=8), A247842 (h=9), A124166 (h=10).

Sequence in context: A050468 A242167 A068778 * A034570 A165963 A221910

Adjacent sequences:  A247814 A247815 A247816 * A247818 A247819 A247820

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Sep 25 2014

STATUS

approved

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Last modified July 27 17:57 EDT 2021. Contains 346308 sequences. (Running on oeis4.)